It's the difference between a first aorist and a second aorist. Just different ways for the same form. The second aorist εἶπον is the older, classical form , but the first aorist εἶπαν is more regular. Similarly with ἦλθον / ἦλθαν. We don't really have enough evidence to get a good feel for the difference beyond that. I would guess that the difference is probably sociolinguistic instead of semantic, with elite writers preferring the traditional second aorist and second language learners perhaps preferring the more regular first aorist.

It's the difference between a first aorist and a second aorist. Just different ways for the same form. The second aorist εἶπον is the older, classical form , but the first aorist εἶπαν is more regular. Similarly with ἦλθον / ἦλθαν. We don't really have enough evidence to get a good feel for the difference beyond that. I would guess that the difference is probably sociolinguistic instead of semantic, with elite writers preferring the traditional second aorist and second language learners perhaps preferring the more regular first aorist.

In antiquity, the various Greek dialects kept 'a' separate from 'o'. The closest vowel to 'a' was 'ω' but 'ω' merged with 'o' before New Testament times and 'a' was always kept distinct from 'o' .

There is one dialect HOWEVER where 'a' and 'o' are confused and that is in "American Seminary Greek, southern and general variety." Please do not perpetrate this. It is hard on Greek ears, especially when students sing with an smile, unknowingly in good Doric song-language Greek, "bless the female goddess," εὐλογεῖτε τὰν θεάν instead of εὐλογεῖτε τὸν θεόν [pronouncing 'tan thean' ].

In antiquity, the various Greek dialects kept 'a' separate from 'o'. The closest vowel to 'a' was 'ω' but 'ω' merged with 'o' before New Testament times and 'a' was always kept distinct from 'o' .

There is one dialect HOWEVER where 'a' and 'o' are confused and that is in "American Seminary Greek, southern and general variety." Please do not perpetrate this. It is hard on Greek ears, especially when students sing with an smile, unknowingly in good Doric song-language Greek, "bless the female goddess," εὐλογεῖτε τὰν θεάν instead of εὐλογεῖτε τὸν θεόν [pronouncing 'tan thean' ].

Well, that is what I had thought as well. But just to be safe I did a search today and to my surprise I found quite a few examples where ο and α were being swapped.

There also were about 5 other cases where the scribe had put down one and then corrected it to the other. Not to mention scores of other cases that I omitted if the difference was found in the word ending. So coming from such a wide variety of manuscripts, it appears to me that they must have sounded a lot closer to each other than I thought. How do you account for this?

The silence is deafening here. In order to figure out the order of magnitude, I went ahead and did the same search for words where ο and ω were being swapped and found that there were about twice as many cases, but that is somewhat misleading because several of the words were simply repeated more often. I then proceeded to do the same search for words where α and ω were being swapped, and there were hardly any. What do I conclude from this?

1. If you want to believe that ο and ω sounded the same (Buthian pronunciation), I think I can make as good as argument that ο and α sounded the same (Erasmian pronunciation). But since the analysis of the data shows that both substitutions were frequently made, this appears to be contrary to both Erasmian and Buthian pronunciation schemes.
2. Since α and ω were almost never confused for each other, we clearly do not have the case where α = ο = ω. One explanation could be that there is a continuum of sound more along the lines of α < ο < ω, with perhaps ο being slightly closer to ω than to α. Another explanation could be that there was both a long ο and short ο sound, with the long ο similar to ω and the short ο similar to α.
3. When people do these kinds of analysis, I am not sure an adequate distinction is being made between “sounds the same” and “sounds similar to”. Just because one letter is often being confused for another does not necessarily mean that they ever sounded the same, but may only be that they sounded similar to each other. For example, some people would pronounce “ten-o-clock” as “ten ah clock” where others may pronounce it as “ten oh clock”. Here o and a have distinct sounds, but they are similar. If someone were to spell it phonetically (like they did in Koine Greek), some might spell it as “ten-a-clock” and others as “ten-o-clock”, but that does not mean that o and a sounded the same to them.
4. The problem mentioned in #3 could happen if the exemplar manuscript was being read orally and multiple scribes in the room were merely writing it down as they heard it. It also could happen if a scribe was making a visual copy and internally rehearsed the words he saw on the page while he transferred his eyes to write it down. The fact that a scribe had written α or ο and later corrected himself to the other on several occasions bears this out.

I'm not Randy Buth, who may be too busy to respond. I do know that his work on this is in line with current scholarship. He's not an idiosyncratic outlier, but rather a fairly mainstream proponent of the field as it currently exists. The work on Koine phonology is based mainly on the patterns of errors in the papyri and inscriptions, as well as on an understanding of the larger diachronic processes in the long, documented history of Greek. In other words, Buth's conclusions rest on a large body of evidence and analysis that is too large to be presented in a forum.

That is why the apparent counter-examples you can (impressively) pull up from the manuscripts of the third and later centuries do not have a strong bearing on the question of Koine-era phonology. Basically, they are more "noise" than "signal" concerning scribal pronunciation, particularly in regard to much more common interchanges between ει and ι, or αι and ε, or even η and ει.

That said, there are other, independently attested, processes going on that may account for at least of the apparent counter-examples.

For example, the variable α and ο in Σολομων/Σαλομων reflects an underlying schwa vowel that mapped to different Greek vowels and gave rise to different spelling conventions for the name. Similarly with the variable vowel in Nαζορηνος/Ναζαρηνος.

Forms like παταμῳ, σταμα, οπο are just scribal errors reflecting a progressive vowel assimilation (with πανταθεν in the opposite direction). Indeed the word ἀπό occurs hundreds if not thousands of times in your data sets, so a single misspelling is not likely to reflect something so systematic as a different pronunciation.

Other cases appear to be differences over the linking vowel in compounds when the second noun is feminine (Συροφοινικισσα/Συραφοινικισσα and μεσονυκτιον/μεσανυκτιον). It appears that, very sporadically, some scribes preferred the more feminine linking vowel -α-.

So, although it is impressive that you can easily pull up the counter-examples, the counter-examples themselves are not sufficiently impressive in quantity or quality.

In other words, Buth's conclusions rest on a large body of evidence and analysis that is too large to be presented in a forum.

I would hope that that would be the case and would be interested in seeing the data for that. My data set is NT words only found in the papyri, etc., but still firmly in the Koine period. The evidence of α and ο swapping is obviously weak compared to ει and ι, or αι and ε, etc. But to my surprise, the evidence of ο and ω swapping was also fairly weak in comparison and the examples of it don’t seem to be significantly different that the examples of α and ο swapping. Thus, I was a little skeptical and would like to see evidence of why one would be and not the other. You are right that the other cases could be explained by dialect or by a scribe choosing a letter to go with the schwa sound. But then again, the ο and ω swapping examples seemed much the same to me as well. The fact that a scribe wrote α or ο and then corrected it to the other seems to be the stronger evidence for me, although that is not definitive.

The reason this matters to me, is not that I intend to speak it one way or another, but that I am trying to identity all valid forms of words for my lexical entries that are not merely different ways to spell the same word phonetically (which would be considerable). Thus, I have only one primary lexical form for Πειλατος/Πιλατος (with Πειλατος being the more prevalent spelling) because they are simply two different spellings that sounded phonetically the same. But I have two lexical forms for αιτιωμα/αιτιαμα for the same lexeme under the assumption that they were pronounced differently. Thus, should Ναζαρηνοσ/Ναζορηνοσ be considered one lexical form that sounded the same but was spelled two different ways, or two distinct forms (dialects) of the same lexeme that were pronounced differently?

I thought I had this thing all buttoned up with the Buthian ο = ω, and α != ο, but my curiosity caused me to do the searches and now it is not so clear to me. It is easy for me to go one way or the other because I have a program that analyses all words phonetically with a standard set of substitution rules (taking into account Buth’s pronunciation scheme) and adjusting for elision, movable nu, movable sigma, etc., so it is simply a matter of whether I include it as a rule or not. The α != ο rule would only affect about 12 distinct lexical forms, while the ο != ω would affect about 60 distinct lexical forms. Thus, the ο = ω rule is more pervasive, but both of these rules are a drop in the bucket compared to ει and ι, or αι and ε, etc. I guess my question is coming down to order of magnitude of how much evidence is enough to establish a rule, and perhaps my dataset is not sufficient to answer that question. I am still wondering if it is more of a continuum along the lines of α < ο < ω, with perhaps ο being closer to ω than to α. I am hoping Randall Buth will weight in on this, but other feedback is welcome.

Part of what I look at to make that determination is the number of times the word occurs. Most words that are botched like οπο only occur once or maybe twice depending on the nature of the error. But words that violate the phonetic rules and are repeated often enough do get their own lexical entry. If that is the way it was commonly spelled by some scribes, then that is the way they spelled it.